| 1. |
- Beneitez Galan, Miguel, et al.
(författare)
-
Edge manifold as a Lagrangian coherent structure in a high-dimensional state space
- 2020
-
Ingår i: Physical Review Research. - : American Physical Society (APS). - 2643-1564. ; 2:3
-
Tidskriftsartikel (refereegranskat)abstract
- Dissipative dynamical systems characterized by two basins of attraction are found in many physical systems, notably in hydrodynamics where laminar and turbulent regimes can coexist. The state space of such systems is structured around a dividing manifold called the edge, which separates trajectories attracted by the laminar state from those reaching the turbulent state. We apply here concepts and tools from Lagrangian data analysis to investigate this edge manifold. This approach is carried out in the state space of autonomous arbitrarily high-dimensional dissipative systems, in which the edge manifold is reinterpreted as a Lagrangian coherent structure (LCS). Two different diagnostics, finite-time Lyapunov exponents and Lagrangian descriptors, are used and compared with respect to their ability to identify the edge and their scalability. Their properties are illustrated on several low-order models of subcritical transition of increasing dimension and complexity, as well on well-resolved simulations of the Navier-Stokes equations in the case of plane Couette flow. They allow for a mapping of the global structure of both the state space and the edge manifold based on quantitative information. Both diagnostics can also be used to generate efficient bisection algorithms to approach asymptotic edge states, which outperform classical edge tracking.
|
|
| 2. |
- Beneitez Galan, Miguel, et al.
(författare)
-
Edge tracking in spatially developing boundary layer flows
- 2019
-
Ingår i: Journal of Fluid Mechanics. - : Cambridge University Press. - 0022-1120 .- 1469-7645. ; 881, s. 164-181
-
Tidskriftsartikel (refereegranskat)abstract
- Recent progress in understanding subcritical transition to turbulence is based on the concept of the edge, the manifold separating the basins of attraction of the laminar and the turbulent state. Originally developed in numerical studies of parallel shear flows with a linearly stable base flow, this concept is adapted here to the case of a spatially developing Blasius boundary layer. Longer time horizons fundamentally change the nature of the problem due to the loss of stability of the base flow due to Tollmien-Schlichting (TS) waves. We demonstrate, using a moving box technique, that efficient long-time tracking of edge trajectories is possible for the parameter range relevant to bypass transition, even if the asymptotic state itself remains out of reach. The flow along the edge trajectory features streak switching observed for the first time in the Blasius boundary layer. At long enough times, TS waves co-exist with the coherent structure characteristic of edge trajectories. In this situation we suggest a reinterpretation of the edge as a manifold dividing the state space between the two main types of boundary layer transition, i.e. bypass transition and classical transition.
|
|
| 3. |
|
|
| 4. |
- Beneitez Galan, Miguel, et al.
(författare)
-
Instability of the optimal edge trajectory in the Blasius boundary layer
- 2023
-
Ingår i: Journal of Fluid Mechanics. - : Cambridge University Press (CUP). - 0022-1120 .- 1469-7645. ; 971
-
Tidskriftsartikel (refereegranskat)abstract
- In the context of linear stability analysis, considering unsteady base flows is notoriously difficult. A generalisation of modal linear stability analysis, allowing for arbitrarily unsteady base flows over a finite time, is therefore required. The recently developed optimally time-dependent (OTD) modes form a projection basis for the tangent space. They capture the leading amplification directions in state space under the constraint that they form an orthonormal basis at all times. The present numerical study illustrates the possibility to describe a complex flow case using the leading OTD modes. The flow under investigation is an unsteady case of the Blasius boundary layer, featuring streamwise streaks of finite length and relevant to bypass transition. It corresponds to the state space trajectory initiated by the minimal seed; such a trajectory is unsteady, free from any spatial symmetry and shadows the laminar-turbulent separatrix for a finite time only. The finite-time instability of this unsteady base flow is investigated using the 8 leading OTD modes. The analysis includes the computation of finite-time Lyapunov exponents as well as instantaneous eigenvalues, and of the associated flow structures. The reconstructed instantaneous eigenmodes are all of outer type. They map unambiguously the spatial regions of largest instantaneous growth. Other flow structures, previously reported as secondary, are identified with this method as relevant to streak switching and to streamwise vortical ejections. The dynamics inside the tangent space features both modal and non-modal amplification. Non-normality within the reduced tangent subspace, quantified by the instantaneous numerical abscissa, emerges only as the unsteadiness of the base flow is reduced.
|
|
| 5. |
- Beneitez Galan, Miguel, et al.
(författare)
-
Modeling the collapse of the edge when two transition routes compete
- 2020
-
Ingår i: Physical review. E. - : American Physical Society (APS). - 2470-0045 .- 2470-0053. ; 102:5
-
Tidskriftsartikel (refereegranskat)abstract
- The transition to turbulence in many shear flows proceeds along two competing routes, one linked with finite-amplitude disturbances and the other one originating from a linear instability, as in, e.g., boundary layer flows. The dynamical systems concept of an edge manifold has been suggested in the subcritical case to explain the partition of the state space of the system. This investigation is devoted to the evolution of the edge manifold when linear stability is added in such subcritical systems, a situation poorly studied despite its prevalence in realistic fluid flows. In particular, the fate of the edge state as a mediator of transition is unclear. A deterministic three-dimensional model is suggested, parametrized by the linear instability growth rate. The edge manifold evolves topologically, via a global saddle-loop bifurcation of the underlying invariant sets, from the separatrix between two attraction basins to the mediator between two transition routes. For larger instability rates, the stable manifold of the saddle point increases in codimension from 1 to 2 after an additional local pitchfork node bifurcation, causing the collapse of the edge manifold. As the growth rate is increased, three different regimes of this model are identified, each one associated with a flow case from the recent hydrodynamic literature. A simple nonautonomous generalization of the model is also suggested in order to capture the complexity of spatially developing flows.
|
|
| 6. |
- Beneitez Galan, Miguel
(författare)
-
Nonlinear dynamics in transitional wall-bounded flows
- 2021
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis focuses on numerical studies of subcritical transition to turbulence in shear flows. The thesis employs a framework based on nonlinear dynamics in the subsequent studies. The geometrical approach to subcritical transition pivots the concepts of edge manifold and edge state. Such concepts are explored in detail in the Blasius boundary layer. The identified edge trajectory is chaotic and presents a couple of high- and low-speed streaks akin to those identified in other shear flows. For long enough times the linear instability of the Blasiusboundary layer coexists with the bypass transition scenario. The edge is thus reinterpreted as a manifold separating both routes. On the edge manifold of the Blasius boundary layer, the fully localised minimal seed is identified. The minimal seed experiences a sequence of linear mechanisms: the Orr mechanism followed by the lift-up. The resulting perturbation approaches the same region in state space as identified from arbitrary perturbations.These insights from the edge trajectory identified in the Blasius boundary layer inspired a low-dimensional model. The model illustrates the e↵ect of the laminar attractor becoming linearly unstable and it agrees qualitatively withother recent studies in the literature.The edge has been identified as a hyperbolic Lagrangian coherent structure of infinite dimension. We show how two Lagrangian diagnostics can be used to locate the edge directly in state space. This allows us to revisit edge tracking as a method optimising a Lagrangian diagnostic instead of a binary algorithm.The two last studies of the thesis focus on the optimally time-dependent(OTD) modes as a basis for the linearised dynamics about a base flow with arbitrary time-dependence. The OTD modes are explored for a periodic flow in pulsating plane Poiseuille flow. The resulting OTD modes can be linked to thespectrum of the Orr-Sommerfeld operator. The results revealed perturbations which span more than one period of the base flow. Finally, the OTD frameworkis used on the edge trajectory starting from the minimal seed in the Blasiusboundary layer.
|
|
| 7. |
- Brandt, Luca, et al.
(författare)
-
Nonlinear optimal perturbations in plane Couette flow
- 2009
-
Ingår i: ADVANCES IN TURBULENCE XII. - Berlin, Heidelberg : Springer Berlin Heidelberg. ; , s. 85-88
-
Konferensbidrag (refereegranskat)abstract
- Subcritical transition to turbulence can occur in a variety of wall-bounded shear flows when the laminar base state is not subject to linear instability. In this case, perturbations to the base state with a finite but very small amplitude can be amplified by non-normal effects, up to a level where nonlinear interactions come into play. Since transition is often undesired, leading to a dramatic increase in wall drag, it is important to know which kind of (weak) perturbations are susceptible to trigger it if we wish to delay it. A vast amount of litterature has described the linear mechanisms responsible for disturbance amplification. Optimisation methods have yielded linear optimal disturbances[1, 2], the disturbances which exhibit the largest linear growth. Yet the focus has been on linear amplification rather than on actual transition, which requires full nonlinearity to be taken into account. In this study, we go back to the original question of which perturbation is most likely to trigger transition to turbulence. We are hence investigating nonlinear optimal disturbances, those with smallest initial energy which effectively lead to a highly disordered flow. In the recent years, progress in the understanding of subcritical transition was made using the concept of ’edge states’, originating from dynamical systems theory. ’Edge state’ refers to the flow regime reached asymptotically by critical trajectories at the exact onset of transition. It is an unstable flow state and cannot be observed in experiments, but its stable manifold determines the basin of attraction of the base state. Direct numerical simulation in minimal domains of plane Couette flow has shown that the flow at the onset of transition asymptotically approaches an unstable finite-amplitude steady state solution, characterised by wavy streaks and streamwise rolls [3]. Using a shooting method, approach to such steady states is the way to characterise whether a transitional trajectory in phase space is actually an ’edge’ trajectory.
|
|
| 8. |
- Brethouwer, Geert, et al.
(författare)
-
Numerical study of turbulent-laminar patterns in MHD, rotating and stratified shear flows
- 2011
-
Ingår i: Direct and Large-Eddy Simulation VIII. - Dordrecht : Springer Netherlands. ; , s. 125-130
-
Konferensbidrag (refereegranskat)abstract
- Coexisting laminar and turbulent regions have been observed in several types of wall bounded flows. In Taylor Couette flow, for example, alternating helical shaped laminar and turbulent regions have been observed within a limited Reynolds number range (Prigent et al., 2002) and oblique laminar and turbulent bands have been seen in experiments (Prigent et al., 2002) and simulations (Barkley and Tuckerman, 2005), (Duguet et al., 2010) of plane Couette flow for Reynolds numbers Re=U w h/ν between about 320 and 380. Here ±U w is the velocity of the two walls, h is the half width of the wall gap and ν is the viscosity. In this Reynolds number range the turbulent-laminar patterns seem to sustain while at lower Re the flow becomes fully laminar and at higher Re no clear laminar patterns can be distinguished and the flow eventually becomes fully turbulent. Similar oblique laminar-turbulent bands appeared as well in direct numerical simulations (DNS) of plane channel flow for friction Reynolds numbers Re τ =u τ h/ν=60 and 80 (Fukudome et al., 2009), (Tsukahara, 2010), where u τ is the friction velocity and h is again the gap half width.
|
|
| 9. |
- Brethouwer, Geert, et al.
(författare)
-
Recurrent Bursts via Linear Processes in Turbulent Environments
- 2014
-
Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 112:14, s. 144502-
-
Tidskriftsartikel (refereegranskat)abstract
- Large-scale instabilities occurring in the presence of small-scale turbulent fluctuations are frequently observed in geophysical or astrophysical contexts but are difficult to reproduce in the laboratory. Using extensive numerical simulations, we report here on intense recurrent bursts of turbulence in plane Poiseuille flow rotating about a spanwise axis. A simple model based on the linear instability of the mean flow can predict the structure and time scale of the nearly periodic and self-sustained burst cycles. Poiseuille flow is suggested as a prototype for future studies of low-dimensional dynamics embedded in strongly turbulent environments.
|
|
| 10. |
- Duguet, Yohann, et al.
(författare)
-
Formation of turbulent patterns near the onset of transition in plane Couette flow
- 2010
-
Ingår i: Journal of Fluid Mechanics. - 0022-1120 .- 1469-7645. ; 650, s. 119-129
-
Tidskriftsartikel (refereegranskat)abstract
- The formation of turbulent patterns in plane Couette flow is investigated near the onset of transition, using numerical simulation in a very large domain of size 800 h x 2h x 356 h. Based on a maximum observation time of 20 000 inertial units, the threshold for the appearance of sustained turbulent motion is Re-c = 324 +/- 1. For Re-c < Re <= 380, turbulent-banded patterns form, irrespective of whether the initial perturbation is a noise or localized disturbance. Measurements of the turbulent fraction versus Re show evidence for a discontinuous phase transition scenario where turbulent spots play the role of the nuclei. Using a smaller computational box, the angle selection of the turbulent bands in the early stages of their development is shown to be related to the amplitude of the initial perturbation.
|
|
